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Related to one-up: One upmanship
tr.v. one-upped, one-up·ping, one-ups Informal
To keep one step ahead of (a competitor or opponent, for example).
informal having or having scored an advantage or lead over someone or something
having gained an advantage, esp. over a rival.
v.t. -upped, -up•ping.
to gain an advantage over; be a move, step, etc., ahead of: to one-up the competition.